Continuation of work on adaptive designs and stochastic approximation methods in simple and multiple regression when the objective is to approach as rapidly as possible some desired optimal value of the control variables so as to minimize the variations of the response around some desired optimal value while still obtaining an efficient estimate of the optimal solution. Asymptotic results for large N and computer simulation for small N of a method for designing sequential clinical trials to choose the better of two treatments, when the objective is to maximize the expected benefit to a known patient horizon N, rather than to estimate the difference between the two treatments without regard to the cost to the patients in the trial group. Sequential design of a trial, with desired operating characteristics for the error probability and smaller expected sample size than for convential methods, when a new treatment is to be compared with a standard and it is desired to adopt the new treatment (because of other advantages) when in fact it is as good or better than the standard.